The cryptographic techniques are the core and foundation for information security and are widely applied to the fields of network communications, electronic commerce, banks and national defence and military. The cryptographic techniques comprise symmetric cryptography and asymmetric cryptography which is also referred to as public key cryptography.
At present, the security of the public key cryptography is mainly dependent on hard problems of large integer factorization and discrete logarithm solving, and the like, such as RSA, ECC, etc. However, after methods capable of implementing large integer factorization and discrete logarithm solving on quantum computers are proposed, this type of traditional public key cryptography has faced a huge threat, and various industries have been affected. Therefore, people have been working to find a cryptographic system capable of protecting against attacks from the quantum computers so as to satisfy the requirement of information security, and this type of system is called post quantum cryptography, one of which is the multivariable public key cryptography.
MPKC plays an important role in the post quantum encryption schemes. The existing MPKC schemes are almost insecure, because a randomly designed quadratic equation has no threshold, and thus it cannot be used for encryption. However, for a mathematical structure generated by a corresponding centralizing mapping, the centralizing mapping thereof can generally be obtained by derivation (i.e. no hiding), such that many MPKC schemes are not only on the basis of MQ problems, there are also structural problems, such as MI, Square, triangular schemes, and the like. Therefore, it is very important for MPKC scheme designing to design a centralizing mapping which is hiding, but has a threshold. At present, schemes designed in this way comprise HFE, ABC, and the like. Although there exists hiding in the centralizing mapping of the former, due to the needs of decryption, the rank of a matrix corresponding to the entire mapping is made very small, rendering it not being able to protect against rank attacks. With respect to the latter, due to the randomness of the centralizing mapping, there is no relevant attacking methods cracking it at present. However, also due to the randomness of the centralizing mapping, it cannot be absolutely decrypted successively, even if it emphasizes that the probability of success decryption can be made very high by setting parameters, for a cryptographic system, this is still not suitable.
As for MPKC schemes, one common technique is the “large field technique”, that is, a public key is map to a large field K, and then vector isomorphism is used (isomorphism is needed). This method is a double-edged sword, because the structure of K makes decryption easy, but such a structure is also easily used by the attackers.